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Estimation of Sky Thermal Irradiance in Arid Climate under Clear Sky Conditions

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Abstract

The sky thermal irradiance (Rsky) is an important factor in meteorological, climatic, and energy balance studies. There are several empirical models for predicting Rsky; however, these are based on the meteorological parameters measured in non-arid climatic conditions and an empirical model for predicting Rsky in arid climates is unavailable. Therefore, this study presents two empirical models for predicting the Rsky under clear sky conditions, common in arid regions such as the Arabian Peninsula. One is based on the sky equivalent emissivity (εsky-model) and the other on the sky equivalent temperature (Tsky-model). Meteorological parameters (i.e., air temperature, relative humidity, solar radiation, and downward Rsky) were measured over 3 years and used to develop and validate the proposed models. The results showed that the proposed εsky- and Tsky-models had the highest predictive accuracy with a coefficient of determination of 0.86 compared with previously published models. In addition, the proposed εsky- and Tsky-models resulted in low values of root mean square and mean absolute percentage errors (7.2 and 7.8 W·m−2 and 1, 2 %, respectively); they were able to precisely predict Rsky at any time in a clear arid climate compared with the prohibitive and time-consuming measurements.

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Abbreviations

c :

Cloud cover factor

G :

Daily integral of global solar radiation flux (kW·h·m−2)

G th :

Daily integral of theoretical solar radiation outside the atmosphere (kW·h·m−2)

MAPE:

Mean absolute percentage error (%)

Pa :

Atmospheric pressure (hPa)

P w :

Water vapor pressure (hPa)

R2 :

Coefficient of determination (%)

R meas :

Measured sky thermal irradiance (W·m−2)

RMSE:

Root mean square error (W·m−2)

Rpred :

Predicted sky thermal irradiance (W·m−2)

R sky :

Sky thermal irradiance under all conditions (W·m−2)

R sky-c :

Clear sky thermal irradiance (W·m−2)

SR :

Solar radiation flux measured in a horizontal plan (W·m−2)

T a :

Ambient air temperature (°C or K)

T sky :

Equivalent sky temperature (K)

εsky :

Equivalent sky emissivity (–)

Ф:

Relative humidity (%)

σ:

Stefan–Boltzmann constant (5.67 × 10−8 W·m−2·K−4)

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Acknowledgments

The authors would like to extend their sincere appreciation to the Deanship of Scientific Research at King Saud University for funding this research through research group number RG 1435-074.

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Authors and Affiliations

  1. Institute of Environment and Sustainable Development in Agriculture, Chinese Academy of Agricultural Sciences, Beijing, 100081, China

    H. A. Ahmed, T. Yu-xin & Y. Qi-chang

  2. Key Laboratory for Energy Saving and Waste Disposal of Protected Agriculture, Ministry of Agriculture, Beijing, 100081, China

    H. A. Ahmed, T. Yu-xin & Y. Qi-chang

  3. Department of Agricultural Engineering, College of Food and Agriculture Sciences, King Saud University, P.O. Box 2460, Riyadh, 11451, Saudi Arabia

    H. A. Ahmed, I. M. Al-Helal, M. R. Shady & A. M. Abdel-Ghany

  4. Department of Agricultural Engineering, Faculty of Agriculture, Sana’a University, Sana’a City, Yemen

    H. A. Ahmed

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  1. H. A. Ahmed
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  2. T. Yu-xin
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  3. Y. Qi-chang
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  4. I. M. Al-Helal
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  5. M. R. Shady
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  6. A. M. Abdel-Ghany
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Correspondence to A. M. Abdel-Ghany.

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Ahmed, H.A., Yu-xin, T., Qi-chang, Y. et al. Estimation of Sky Thermal Irradiance in Arid Climate under Clear Sky Conditions. Int J Thermophys 41, 76 (2020). https://doi.org/10.1007/s10765-020-02656-1

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